Question

Let l be the length of a diagonal of a rectangle whose sides have lengths z and y. If z increases at a constant rate of -f/s and y decreases at a constant rate of f/s, how fast is the size of the diagonal changing when t = 3s and y = 6 ft?

a) -3√5 ft/s
b) 3√5 ft/s
c) -6√5 ft/s
d) 6√5 ft/s

Answer 1

To find the rate at which the size of the diagonal is changing, we can differentiate the formula for the length of the diagonal with respect to time and plug in the given values.

Step-by-step explanation:

To find how fast the size of the diagonal is changing, we need to differentiate the formula for the length of the diagonal with respect to time. The formula for the length of the diagonal of a rectangle is √(z^2 + y^2). Taking the derivative with respect to time, we have dL/dt = (1/2)(2z dz/dt + 2y dy/dt). Given that dz/dt = -f/s and dy/dt = -f/s, we can plug in the values and solve for dL/dt when z = 3s and y = 6ft.